Xe-124 an isotope of xenon has the highest half-life of 1.8 × 1022 yrs. Estimate the time it would take for a sample of Xe-124 to reach 10% of its current level.
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- When a nucleus becomes unstable it will undergo radioactive decay to attain a stable configuration. They do so by emitting radiation.
- The rate of radioactive decay is called activity and the half-life is the time it takes for the activity to reduce by half in a radioactive sample.
- Radioactive decay is exponential in nature and can be written as,
Here N0 is the original number of radioactive nuclei present, t is the time, and t1/2 is the half-life of the radioactive sample. This is known as the exponential law of radioactive decay.
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- The half-life for the decay of carbon-14 is 5.73*10^3 years. Suppose the activity due to the radioactive decay of the carbon-14 in a tiny sample of an artifact made of wood from an archeological dig is measured to be 1.0*10^ 3Bq. The activity in a similar-sized sample of fresh wood is measured to be 6.9*10^3 Bq. Calculate the age of the artifact. Round your answer to 2 significant digits.The activity of C-14 can be used to determine the age of some archaeological discoveries. Suppose a sample of ancient wood which contains C-14 has an activity of 7.50 x 10^-4 Ci. The half life of C-14 is 5730 years. What will be the activity of this sample after 250 years?The amount of carbon-14 found in a fossil of a tree is around 0.05% when compared to fresh wood of the same kind. Estimate the age of the fossil.
- Modern household smoke detectors contain a tiny speck of the element Americium (Am, atomic number 95, atomic mass 241), which has a half-life of 432 years and an activity of (roughly) of 37,000 decays per second. a) What is the approximate mass of this speck? (Hint: the atomic mass of this isotope is approximately 241.06 u). b) This isotope is an alpha emitter. Is its radiation likely to be a hazard to the household members while the smoke detector is on the ceiling? Explain.Carbon-14, with a half-life of 5730 years, has a decay constant of λ = 1.21 × 10-4 yr-1. A piece of wood from an archaeological site is found to have 1.9 % of its original carbon-14. How many years old (t) is the piece of wood? Express your answer in scientific notation. Example: 1.23e4.Calculate the binding energy per nucleon of the carbon nucleus, 612?. (Given mass of proton = 1.007276 u, mass of neutron = 1.008665 u, mass of electron = 0.000549 u and mass of Carbon-12 atom = 12.000000 u)
- You inherit 32 kg of cesium-136 after your roommate moves out and leaves it behind. Cesium-137 has a half-life of 30 years. If you pack it in a box and forget about it, but your grandchildren finds it in the attic 90 years from now, how much of the sample is still cesium-137?The isotope ¹C has a half-life of 5730 years. What percent (N/No) of the ¹4C in a buried animal 14 bone will remain after 45,000 years?The binding energy for a nucleus containing Z protons and N neutrons is defined as c²[ZM + Nm, - M] where M is the mass of the neutral atom containing the nucleus, the quantity in the parentheses is the mass defect, and c? = 931.5 MeV/u.The binding energy of a nuclide can also be written as E, = Am x 931.5 MeV/u where Am is the mass defect. The Figure below show the mass for neutral atom and the nucleons of a helium atom. SHe Binding energy Mass = 4.0026 u Mass = 4.0330 u Calculate the mass defect Am of a helium atom